New Frontiers in Machine Learning and Quantum

Gibbs Sampling of Periodic Potentials on a Quantum Computer

Nov 23, 2022, 4:00 p.m.

30m

PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)

Speaker

Arsalan Motamedi (University of Waterloo)

Description

"Motivated by applications in machine learning, we present a quantum algorithm for Gibbs sampling from continuous real-valued functions defined on high dimensional tori. We show that these families of functions satisfy a Poincare inequality. We then use the techniques for solving linear systems and partial differential equations to design an algorithm that performs zeroeth order queries to a quantum oracle computing the energy function to return samples
from its Gibbs distribution. We further analyze the query and gate complexity of our algorithm and prove that the algorithm has a polylogarithmic dependence on approximation error (in total variation distance) and a polynomial dependence on the number of variables, although it suffers from an exponentially poor dependence on temperature."

External references

• 22110094
• 7da2185e-5dee-4216-b02b-a1097dc6fa59
• 59cca86e-009e-4d00-b848-f66642d66680